Markov Chain

A Markov chain is a sequence of Probability Vectors, and a Stochastic Matrix P , such that:

$$\begin{array}{c}{P}^k\overrightarrow{x_0}={\vec{x}}_k\\ {\vec{x}}_{k+1}=P{\vec{x}}_k\\ k\in {\mathbb{N}}_0\end{array}$$